Also number of score sequences of length n: weakly increasing sequences a[0,1,...,n-1] where sum(j=0..k, a[j]) >= k*(k+1)/2 and sum(j=0..n-1, a[j]) = (n-1)*n/2; same as weak compositions of n*(n-1) with partial sums up to position k at least k*(k+1)/2; see example. - Joerg Arndt, Mar 29 2014